Microwave instability beyond threshold.

Abstract

Stability of the steady-state bunch distribution described by the Haissinski solution [J. Haissinski, Nuovo Cimento {bold 18B}, 72 (1973)] is studied above the threshold of microwave instability. It is shown that instability may lead to a new self-consistent state corresponding to particles trapped in a separatrix of an unstable mode. The free energies of the two solutions are compared. The relaxation oscillations between the new and Haissinski solutions are possible and may be related to the sawtooth instability observed recently in the experiments [P. Krejcik {ital et} {ital al}., (unpublished)]. {copyright} {ital 1996 The American Physical Society.}